This article at Discover Magazine has nothing to do with the science fiction stories we are so familiar with. Author Sean Carroll looks at time travel as a physicist. He says if time travel were possible (and it might be), there would be no paradox, because we cannot change what has already happened. Ever. Then it gets weird.

Imagine that we have been appointed Guardian of the Gate, and our job is to keep vigilant watch over who passes through. One day, as we are standing off to the side, we see a person walk out of the rear side of the gate, emerging from one day in the future. That’s no surprise; it just means that you will see that person enter the front side of the gate tomorrow. But as you keep watch, you notice that he simply loiters around for one day, and when precisely 24 hours have passed, the traveler walks calmly through the front of the gate. Nobody ever approached from elsewhere. That 24-hour period constitutes the entire life span of this time traveler. He experiences the same thing over and over again, although he doesn’t realize it himself, since he does not accumulate new memories along the way. Every trip through the gate is precisely the same to him. That may strike you as weird or unlikely, but there is nothing paradoxical or logically inconsistent about it.

Say your friend dies in a car crash. You travel back in time to save him. Your friend says thanks as you head back to your future. From your friend's point of view, he carries on his life until he reaches the point in time where you jump back in time to save. Except you don't. Because he didn't die. So if he didn't die, you never had to go back in time. And if you never went back in time, then who saved him from being killed in a car crash? Paradox.

(I suppose your friend could manipulate you into time travelling back to save him or just outright ask you to but this contradicts the original reason. Your friend was, as far as you were concerned originally, dead.)

So the only leeway I can see for changing the past is if the exact circumstances are not know. The outcome can never change but the details can.

The quoted story sure looks paradoxical to me. Suppose the time traveler who exited the gate had a beard that was 1 mm long. In the 24 hours he loiters near the gate, it might grow to 2 mm. But clearly he can't be the same man who exited the gate, since the man going in had a 2 mm beard but the man coming out only had a 1 mm beard. I think the author must have forgotten to mention one of his assumptions.

The problem with this theory is that there is no past that can be changed. So if you can travel to say 2013, you can't come back to 2012. Also the person in the story only has a 24 hour life span....He would'nt be a man then. Its not a life span, its a 24hr moment in time. Is it past or present humm?